Given the radius of a sphere is measured as 9 cm with an error of 0.03 m = 3 cm.

Let x be the radius of the sphere and Δx be the error in measuring the value of x.

Hence, we have x = 9 and Δx = 3

The surface area of a sphere of radius x is given by

S = 4πx2

On differentiating S with respect to x, we get

We know

When x = 9, we have.

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δx = 3

ΔS = (72π)(3)

ΔS = 216π

Thus, the approximate error in calculating the surface area of the sphere is 216π cm2.

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